University of Virginia Library

CHAPTER XXXIV
A LAW OF ACCELERATION (1904)

IMAGES are not arguments, rarely even lead to proof, but the
mind craves them, and, of late more than ever, the keenest
experimenters find twenty images better than one, especially
if contradictory; since the human mind has already learned to deal
in contradictions.

The image needed here is that of a new centre, or preponderating
mass, artificially introduced on earth in the midst of a system of
attractive forces that previously made their own equilibrium, and
constantly induced to accelerate its motion till it shall establish a
new equilibrium. A dynamic theory would begin by assuming that
all history, terrestrial or cosmic, mechanical or intellectual, would
be reducible to this formula if we knew the facts.

For convenience, the most familiar image should come first;
and this is probably that of the comet, or meteoric streams, like
the Leonids and Perseids; a complex of minute mechanical agencies,
reacting within and without, and guided by the sum of forces
attracting or deflecting it. Nothing forbids one to assume that the
man-meteorite might grow, as an acorn does, absorbing light,
heat, electricity—or thought; for, in recent times, such transference
of energy has become a familiar idea; but the simplest figure,
at first, is that of a perfect comet—say that of 1843—which
drops from space, in a straight line, at the regular acceleration of
speed, directly into the sun, and after wheeling sharply about it,
in heat that ought to dissipate any known substance, turns back
unharmed, in defiance of law, by the path on which it came.
The mind, by analogy, may figure as such a comet, the better
because it also defies law.

Motion is the ultimate object of science, and measures of motion
are many; but with thought as with matter, the true measure is

mass in its astronomic sense—the sum or difference of attractive
forces. Science has quite enough trouble in measuring its
material motions without volunteering help to the historian, but
the historian needs not much help to measure some kinds of social
movement; and especially in the nineteenth century, society
by common accord agreed in measuring its progress by the coal-output.
The ratio of increase in the volume of coal-power may
serve as dynamometer.

The coal-output of the world, speaking roughly, doubled every
ten years between 1840 and 1900, in the form of utilized power,
for the ton of coal yielded three or four times as much power in
1900 as in 1840. Rapid as this rate of acceleration in volume seems,
it may be tested in a thousand ways without greatly reducing it.
Perhaps the ocean steamer is nearest unity and easiest to measure,
for any one might hire, in 1905, for a small sum of money, the use
of 30,000 steam-horse-power to cross the ocean, and by halving
this figure every ten years, he got back to 234 horse-power for
1835, which was accuracy enough for his purposes. In truth, his
chief trouble came not from the ratio in volume of heat, but from
the intensity, since he could get no basis for a ratio there. All
ages of history have known high intensities, like the iron-furnace,
the burning-glass, the blow-pipe; but no society has ever used
high intensities on any large scale till now, nor can a mere bystander
decide what range of temperature is now in common use.
Loosely guessing that science controls habitually the whole range
from absolute zero to 3000° Centigrade, one might assume, for
convenience, that the ten-year ratio for volume could be used temporarily
for intensity; and still there remained a ratio to be guessed
for other forces than heat. Since 1800 scores of new forces had been
discovered; old forces had been raised to higher powers, as could
be measured in the navy-gun; great regions of chemistry had
been opened up, and connected with other regions of physics.
Within ten years a new universe of force had been revealed in
radiation. Complexity had extended itself on immense horizons,

and arithmetical ratios were useless for any attempt at accuracy.
The force evolved seemed more like explosion than gravitation,
and followed closely the curve of steam; but, at all events, the tenyear
ratio seemed carefully conservative. Unless the calculator
was prepared to be instantly overwhelmed by physical force and
mental complexity, he must stop there.

Thus, taking the year 1900 as the starting point for carrying back
the series, nothing was easier than to assume a ten-year period of
retardation as far back as 1820, but beyond that point the statistician
failed, and only the mathematician could help. Laplace
would have found it child's-play to fix a ratio of progression in
mathematical science between Descartes, Leibnitz, Newton, and
himself. Watt could have given in pounds the increase of power
between Newcomen's engines and his own. Volta and Benjamin
Franklin would have stated their progress as absolute creation
of power. Dalton could have measured minutely his advance on
Boerhaave. Napoleon I must have had a distinct notion of his
own numerical relation to Louis XIV. No one in 1789 doubted the
progress of force, least of all those who were to lose their heads
by it.

Pending agreement between these authorities, theory may
assume what it likes—say a fifty, or even a five-and-twenty-year
period of reduplication for the eighteenth century, for the period
matters little until the acceleration itself is admitted. The subject
is even more amusing in the seventeenth than in the eighteenth
century, because Galileo and Kepler, Descartes, Huygens,
and Isaac Newton took vast pains to fix the laws of acceleration
for moving bodies, while Lord Bacon and William Harvey were
content with showing experimentally the fact of acceleration in
knowledge; but from their combined results a historian might be
tempted to maintain a similar rate of movement back to 1600,
subject to correction from the historians of mathematics.

The mathematicians might carry their calculations back as far
as the fourteenth century when algebra seems to have become for

the first time the standard measure of mechanical progress in
western Europe; for not only Copernicus and Tycho Brahe, but
even artists like Leonardo, Michael Angelo, and Albert Dürer
worked by mathematical processes, and their testimony would
probably give results more exact than that of Montaigne or Shakespeare;
but, to save trouble, one might tentatively carry back the
same ratio of acceleration, or retardation, to the year 1400, with
the help of Columbus and Gutenberg, so taking a uniform rate
during the whole four centuries (1400–1800), and leaving to statisticians
the task of correcting it.

Or better, one might, for convenience, use the formula of
squares to serve for a law of mind. Any other formula would do
as well, either of chemical explosion, or electrolysis, or vegetable
growth, or of expansion or contraction in innumerable forms; but
this happens to be simple and convenient. Its force increases in
the direct ratio of its squares. As the human meteoroid approached
the sun or centre of attractive force, the attraction of one century
squared itself to give the measure of attraction in the next.

Behind the year 1400, the process certainly went on, but the
progress became so slight as to be hardly measurable. What
was gained in the east or elsewhere, cannot be known; but forces,
called loosely Greek fire and gunpowder, came into use in the west
in the thirteenth century, as well as instruments like the compass,
the blow-pipe, clocks and spectacles, and materials like paper;
Arabic notation and algebra were introduced, while metaphysics
and theology acted as violent stimulants to mind. An architect
might detect a sequence between the Church of St. Peter's at
Rome, the Amiens Cathedral, the Duomo at Pisa, San Marco
at Venice, Sancta Sofia at Constantinople and the churches at
Ravenna. All the historian dares affirm is that a sequence is manifestly
there, and he has a right to carry back his ratio, to represent
the fact, without assuming its numerical correctness. On the
human mind as a moving body, the break in acceleration in the
Middle Ages is only apparent; the attraction worked through

shifting forms of force, as the sun works by light or heat, electricity,
gravitation, or what not, on different organs with different
sensibilities, but with invariable law.

The science of prehistoric man has no value except to prove
that the law went back into indefinite antiquity. A stone arrowhead
is as convincing as a steam-engine. The values were as clear
a hundred thousand years ago as now, and extended equally over
the whole world. The motion at last became infinitely slight, but
cannot be proved to have stopped. The motion of Newton's comet
at aphelion may be equally slight. To evolutionists may be left
the processes of evolution; to historians the single interest is the
law of reaction between force and force—between mind and
nature—the law of progress.

The great division of history into phases by Turgot and Comte
first affirmed this law in its outlines by asserting the unity of progress,
for a mere phase interrupts no growth, and nature shows
innumerable such phases. The development of coal-power in the
nineteenth century furnished the first means of assigning closer
values to the elements; and the appearance of supersensual forces
towards 1900 made this calculation a pressing necessity; since the
next step became infinitely serious.

A law of acceleration, definite and constant as any law of mechanics,
cannot be supposed to relax its energy to suit the convenience
of man. No one is likely to suggest a theory that man's
convenience had been consulted by Nature at any time, or that
Nature has consulted the convenience of any of her creations, except
perhaps the Terebratula. In every age man has bitterly and
justly complained that Nature hurried and hustled him, for inertia
almost invariably has ended in tragedy. Resistance is its law, and
resistance to superior mass is futile and fatal.

Fifty years ago, science took for granted that the rate of acceleration
could not last. The world forgets quickly, but even today
the habit remains of founding statistics on the faith that
consumption will continue nearly stationary. Two generations,

with John Stuart Mill, talked of this stationary period, which
was to follow the explosion of new power. All the men who were
elderly in the forties died in this faith, and other men grew old
nursing the same conviction, and happy in it; while science, for
fifty years, permitted, or encouraged, society to think that force
would prove to be limited in supply. This mental inertia of science
lasted through the eighties before showing signs of breaking
up; and nothing short of radium fairly wakened men to the fact,
long since evident, that force was inexhaustible. Even then the
scientific authorities vehemently resisted.

Nothing so revolutionary had happened since the year 300.
Thought had more than once been upset, but never caught and
whirled about in the vortex of infinite forces. Power leaped from
every atom, and enough of it to supply the stellar universe showed
itself running to waste at every pore of matter. Man could no
longer hold it off. Forces grasped his wrists and flung him about
as though he had hold of a live wire or a runaway automobile;
which was very nearly the exact truth for the purposes of an elderly
and timid single gentleman in Paris, who never drove down
the Champs Elysées without expecting an accident, and commonly
witnessing one; or found himself in the neighborhood of an official
without calculating the chances of a bomb. So long as the
rates of progress held good, these bombs would double in force
and number every ten years.

Impossibilities no longer stood in the way. One's life had fattened
on impossibilities. Before the boy was six years old, he had
seen four impossibilities made actual—the ocean-steamer, the
railway, the electric telegraph, and the Daguerreotype; nor could
he ever learn which of the four had most hurried others to come.
He had seen the coal-output of the United States grow from nothing
to three hundred million tons or more. What was far more
serious, he had seen the number of minds, engaged in pursuing
force—the truest measure of its attraction—increase from a
few scores or hundreds, in 1838, to many thousands in 1905,

trained to sharpness never before reached, and armed with instruments
amounting to new senses of indefinite power and accuracy,
while they chased force into hiding-places where Nature herself
had never known it to be, making analyses that contradicted
being, and syntheses that endangered the elements. No one
could say that the social mind now failed to respond to new force,
even when the new force annoyed it horribly. Every day Nature
violently revolted, causing so-called accidents with enormous
destruction of property and life, while plainly laughing at man, who
helplessly groaned and shrieked and shuddered, but never for a
single instant could stop. The railways alone approached the carnage
of war; automobiles and fire-arms ravaged society, until
an earthquake became almost a nervous relaxation. An immense
volume of force had detached itself from the unknown universe
of energy, while still vaster reservoirs, supposed to be infinite,
steadily revealed themselves, attracting mankind with more compulsive
course than all the Pontic Seas or Gods or Gold that ever
existed, and feeling still less of retiring ebb.

In 1850, science would have smiled at such a romance as this,
but, in 1900, as far as history could learn, few men of science
thought it a laughing matter. If a perplexed but laborious follower
could venture to guess their drift, it seemed in their minds
a toss-up between anarchy and order. Unless they should be more
honest with themselves in the future than ever they were in the
past, they would be more astonished than their followers when
they reached the end. If Karl Pearson's notions of the universe
were sound, men like Galileo, Descartes, Leibnitz, and Newton
should have stopped the progress of science before 1700, supposing
them to have been honest in the religious convictions they expressed.
In 1900 they were plainly forced back on faith in a unity
unproved and an order they had themselves disproved. They
had reduced their universe to a series of relations to themselves.
They had reduced themselves to motion in a universe of motions,
with an acceleration, in their own case, of vertiginous violence.

With the correctness of their science, history had no right to meddle,
since their science now lay in a plane where scarcely one or
two hundred minds in the world could follow its mathematical
processes; but bombs educate vigorously, and even wireless telegraphy
or airships might require the reconstruction of society.
If any analogy whatever existed between the human mind, on
one side, and the laws of motion, on the other, the mind had already
entered a field of attraction so violent that it must immediately
pass beyond, into new equilibrium, like the Comet of
Newton, to suffer dissipation altogether, like meteoroids in the
earth's atmosphere. If it behaved like an explosive, it must rapidly
recover equilibrium; if it behaved like a vegetable, it must
reach its limits of growth; and even if it acted like the earlier creations
of energy—the saurians and sharks—it must have nearly
reached the limits of its expansion. If science were to go on doubling
or quadrupling its complexities every ten years, even mathematics
would soon succumb. An average mind had succumbed
already in 1850; it could no longer understand the problem in 1900.

Fortunately, a student of history had no responsibility for the
problem; he took it as science gave it, and waited only to be
taught, With science or with society, he had no quarrel and
claimed no share of authority. He had never been able to acquire
knowledge, still less to impart it; and if he had, at times, felt serious
differences with the American of the nineteenth century, he
felt none with the American of the twentieth. For this new creation,
born since 1900, a historian asked no longer to be teacher or
even friend; he asked only to be a pupil, and promised to be docile,
for once, even though trodden under foot; for he could see
that the new American—the child of incalculable coal-power,
chemical power, electric power, and radiating energy, as well as
of new forces yet undetermined—must be a sort of God compared
with any former creation of nature. At the rate of progress
since 1800, every American who lived into the year 2000 would
know how to control unlimited power. He would think in complexities

unimaginable to an earlier mind. He would deal with problems
altogether beyond the range of earlier society. To him the
nineteenth century would stand on the same plane with the fourth
—equally childlike—and he would only wonder how both of
them, knowing so little, and so weak in force, should have done so
much. Perhaps even he might go back, in 1964, to sit with Gibbon
on the steps of Ara Cœli.

Meanwhile he was getting education. With that, a teacher who
had failed to educate even the generation of 1870, dared not interfere.
The new forces would educate. History saw few lessons in
the past that would be useful in the future; but one, at least, it did
see. The attempt of the American of 1800 to educate the American
of 1900 had not often been surpassed for folly; and since 1800
the forces and their complications had increased a thousand times
or more. The attempt of the American of 1900 to educate the
American of 2000, must be even blinder than that of the Congressman
of 1800, except so far as he had learned his ignorance.
During a million or two of years, every generation in turn had
toiled with endless agony to attain and apply power, all the while
betraying the deepest alarm and horror at the power they created.
The teacher of 1900, if foolhardy, might stimulate; if foolish,
might resist; if intelligent, might balance, as wise and foolish have
often tried to do from the beginning; but the forces would continue
to educate, and the mind would continue to react. All the teacher
could hope was to teach it reaction.

Even there his difficulty was extreme. The most elementary
books of science betrayed the inadequacy of old implements of
thought. Chapter after chapter closed with phrases such as one
never met in older literature: "The cause of this phenomenon is
not understood"; "science no longer ventures to explain causes";
"the first step towards a causal explanation still remains to be
taken"; "opinions are very much divided"; "in spite of the contradictions
involved"; "science gets on only by adopting different
theories, sometimes contradictory." Evidently the new American

would need to think in contradictions, and instead of Kant's
famous four antinomies, the new universe would know no law
that could not be proved by its anti-law.

To educate—one's self to begin with—had been the effort of
one's life for sixty years; and the difficulties of education had gone
on doubling with the coal-output, until the prospect of waiting
another ten years, in order to face a seventh doubling of complexities,
allured one's imagination but slightly. The law of acceleration
was definite, and did not require ten years more study
except to show whether it held good. No scheme could be suggested
to the new American, and no fault needed to be found, or
complaint made; but the next great influx of new forces seemed
near at hand, and its style of education promised to be violently
coercive. The movement from unity into multiplicity, between
1200 and 1900, was unbroken in sequence, and rapid in acceleration,
Prolonged one generation longer, it would require a new social
mind. As though thought were common salt in indefinite solution
it must enter a new phase subject to new laws. Thus far, since
five or ten thousand years, the mind had successfully reacted, and
nothing yet proved that it would fail to react—but it would
need to jump.